Sure, let's go through the process of estimating the product of [tex]\(\frac{7}{8}\)[/tex] and [tex]\(8 \frac{1}{10}\)[/tex] step-by-step:
### Step 1: Understanding the Fractions
First, let's analyze the given fractions:
1. [tex]\(\frac{7}{8}\)[/tex]
2. [tex]\(8 \frac{1}{10}\)[/tex]
### Step 2: Converting the Mixed Number
Next, we need to convert the mixed number [tex]\(8 \frac{1}{10}\)[/tex] into an improper fraction:
[tex]\[ 8 \frac{1}{10} = 8 + \frac{1}{10} = \frac{80}{10} + \frac{1}{10} = \frac{81}{10} \][/tex]
### Step 3: Calculating the Product
Now, we calculate the exact product of [tex]\(\frac{7}{8}\)[/tex] and [tex]\(\frac{81}{10}\)[/tex]:
[tex]\[ \text{Product} = \frac{7}{8} \times \frac{81}{10} = \frac{7 \times 81}{8 \times 10} = \frac{567}{80} \approx 7.09 \][/tex]
### Step 4: Rounding and Estimate
To estimate, we will round each fraction to the nearest whole number:
- [tex]\(\frac{7}{8}\)[/tex] rounds to [tex]\(1\)[/tex] because it is closer to [tex]\(1\)[/tex] than [tex]\(0\)[/tex].
- [tex]\(\frac{81}{10}\)[/tex] (which is [tex]\(8.1\)[/tex]) rounds to [tex]\(8\)[/tex] because it is closer to [tex]\(8\)[/tex] than [tex]\(10\)[/tex].
### Step 5: Calculating the Estimated Product
Using the rounded values, we multiply:
[tex]\[ \text{Estimated Product} = 1 \times 8 = 8 \][/tex]
### Step 6: Selecting the Best Estimate
Given the choices:
- [tex]\( 0 \times 8 = 0 \)[/tex]
- [tex]\( 1 \times 10 = 10 \)[/tex]
- [tex]\( 7 \times 8 = 56 \)[/tex]
- [tex]\( 1 \times 8 = 8 \)[/tex]
Among these options, the expression [tex]\(1 \times 8\)[/tex] provides the best estimate for the actual product, which we have calculated to be approximately [tex]\(7.09\)[/tex].
Therefore, the best estimate of the product of [tex]\(\frac{7}{8}\)[/tex] and [tex]\(8 \frac{1}{10}\)[/tex] is:
[tex]\[ 1 \times 8 \][/tex]
